You need more edges around the ring (in other words, the object needs more "resolution" - not in terms of pixels of course, but in terms of edges), so one option is to use the subdivision modifier. If you use the subdivision modifier make sure to use Supporting Edge Loops around the ring to keep the edge 'sharp' and in place. If you already have the subdivision modifier applied, just increase the number of subdivisions (make sure to set the "render" number of subdivisions - this is the number that will actually be applied when you render the scene).
If you don't want to use subdivision in the whole object you can do it manually: select the ring edge loop and use the subdivide function in edit mode, and then you can use the smooth tool to make it rounder. You'll probably need to do some retopologizing around the ring to deal with Ngons (faces with more than 4 sides that will be created when you subdivide the edges).
PS: at first I thought it was the white plastic part that needed more edges, but looking again at the image it looks like it's the metal part, it's hard to tell without the wireframes. Anyway the answer is still the same, just make sure you apply the solution to the part that needs more edges.
PS2: Keep in mind that you only need to add more resolution to the object if your final image will actually be such an extreme close-up, or else this detail might be imperceptible and you wouldn't have to worry about it.